Summary of the invention
In order to overcome above-mentioned technical disadvantages, the purpose of this invention is to provide a kind of computing method of the part conicity based on Minimum Area.This method has not only improved the precision of surveying instrument detection taperness error, and algorithm stability is good, counting yield is high.
The computing method of a kind of part conicity based on Minimum Area of the present invention when cone angle is variable, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
, wherein
=1,2 ...,
n,
nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Form the measuring point collection
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
, the circular cone axis direction vector
And semi-cone angle
Wherein
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Step 2: use following formula, calculate each measuring point successively
Distance to circular conical surface
,
Wherein
, all measuring point correspondences
Form set
Record respectively
,
Corresponding measuring point, institute's record
Corresponding measuring point forms the low value contact point set of containment region
, institute's record
Corresponding measuring point forms the high value contact point set of containment region
And according to
,
With
, calculate
Coordinate and the interior vertex of a cone that contains circular cone
Coordinate; This moment taperness error
=
Step 3: judge that whether the quantity of low value contact point in the set of low value contact point is less than 2;
If the quantity of low value contact point, is pressed the computing method of maximum inscribed circle awl less than 2, inquire about preceding 2 low value contact points, and calculate the parameter of circular cone, jump to step 2;
If the quantity of low value contact point is carried out next step more than or equal to 2.
Step 4: whether the quantity of judging low value contact point in the set of low value contact point equals 2;
If low value contact point quantity equals 2, then 2 low value contact points are effective contact point;
If low value contact point quantity greater than 2, then connects high value contact point and the outer vertex of a cone that contains circular cone respectively
, connect the vertex of a cone of low value contact point and interior containing circular cone respectively
, calculate successively 2 groups of straight lines with arbitrarily perpendicular to
The intersection point on plane, can judgement find 2 low value contact points, the intersection point that connects 2 low value contact point correspondences obtains straight line
l, the intersection point intersection point corresponding with all the other low value contact points that satisfies high value contact point correspondence is distributed in straight line respectively
lBoth sides, if can not find 2 low value contact points that satisfy condition, then jump to step 6; If can find 2 low value contact points that satisfy condition, 2 low value contact points that then satisfy condition are effective contact point, jump to step 5.
Step 5: the intersection point that connects 2 effective low value contact point correspondences obtains straight line
l 1, and in the corresponding intersection point set of high value contact, inquiry is apart from straight line
l 1Nearest intersection point, then the high value contact point of this intersection point correspondence is effectively high value contact point; 2 effective low value contact points respectively with the vertex of a cone of interior containing circular cone
Link to each other, 2 lines constitute 1 angle, calculate the equidistant point of this angle, and the normal vector of this equidistant point is the direction vector of containment region rotation change
If
Be 1 effective low value contact point wherein,
Be effectively high value contact point;
With 1 noncontact measuring point wherein
Be calculating object, calculate
Equidistant point, and calculate this equidistant point and mistake
And normal vector is
The intersection on plane
, calculate then
Deduct
With
Angle, obtain
Travel through all noncontact measuring points, the calculating correspondence
, all measuring point correspondences
Form set
, in set
Middle element of rejecting less than 0;
Again with a noncontact measuring point
Be calculating object, do
Equidistant point, and calculate this equidistant point and mistake
And normal vector is
The intersection on plane
, calculate then
Deduct
With
Angle, obtain
Travel through all noncontact measuring points, the calculating correspondence
, all measuring point correspondences
Form set
, in set
Middle element of rejecting less than 0;
Query set
,
In minimum value, minimum value is the rotation variation of containment region
On the direction that cone angle reduces, containment region around
Rotation
After, the parameter of calculating containment region
,
,
,
, jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Direction vector
With
zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
,
zAxial coordinate increases progressively, and makes
,
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Or
The rotation variation of containment region is set
Initial value.
Step 7: calculate
Around
Or
Rotation
Vector after the angle
With
,
Be the vertex of a cone, with
For the axis direction vector, with
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
,
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
,
,
,
Shadow is on any a certain plane perpendicular to axis
On, obtain respectively
,
,
,
, will cut and hand over circular projection on the plane
On; Can set up the binary nonlinear system of equations by following relation,
Wherein
,
Be respectively
,
Corresponding cross section radius of circle,
After change
On the plane
Projection; By finding the solution Nonlinear System of Equations, can calculate
Coordinate; According to
,
,
,
With
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
,
According to the method for step 2, calculate the low value contact point contains circular cone outside containment region distance
, calculate high value contact point contains circular cone outside containment region distance
And then according to the method for step 2, calculate all noncontact measuring points contain circular cone outside containment region distance successively
If
And
, then represent the variation deficiency, the anglec of rotation
Become
If
Or
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Become
Judge
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
If
The difference of the iterative value that front and back are 2 times is less than the error permissible value
, illustrate and find the 5th contact point, then will
,
,
Assignment is given respectively
,
,
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
,
, then each low value contact point all satisfies following formula,
Each low value contact point all satisfies following formula,
More than in two formulas
,
,
With
,
,
,
,
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge whether high value contact equals 6 with low value contact point quantity sum;
If high value contact is not equal to 6 with low value contact point quantity sum; Jump to step 12; Otherwise carry out dimensional variations, set the dimensional variations amount
Initial value.
Step 11: the method in the applying step 9, with
,
,
,
,
,
Be unknown quantity, set up Nonlinear System of Equations, error of calculation containment region width is
The time the containment region parameter;
The method of applying step 7 has judged whether that according to change back containment region parameter measuring point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If less than, illustrate and find the 7th contact point, jump to step 12; Otherwise, carry out dimensional variations again, the operation of repeating step 11.
Step 12: judge that whether high value contact and low value contact point quantity sum are more than or equal to 7;
If high value contact and low value contact point contact point quantity sum are more than or equal to 7, with in the contact point set 6 be 1 combination, be calculating object with 6 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 10,11 is adjusted
Size; If
Less than the error permissible value of setting
, judge whether to satisfy criterion, jump to step 13 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
, judge that again iteration is gone down successively; If
Greater than the error permissible value of setting
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 7.
Step 13: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Another kind of the present invention is based on the computing method of the part conicity of Minimum Area, and when cone angle was constant, the calculation process when being variable with cone angle was similar substantially, and difference is to keep cone angle constant in the containment region change, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
, wherein
=1,2 ...,
n,
nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Form the measuring point collection
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
, the circular cone axis direction vector
According to drawing information, obtain semi-cone angle
Wherein
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Step 2: use following formula, calculate each measuring point successively
Distance to circular conical surface
,
Wherein
, all measuring point correspondences
Form set
Record respectively
,
Corresponding measuring point, institute's record
Corresponding measuring point forms the low value contact point set of containment region
, institute's record
Corresponding measuring point forms the high value contact point set of containment region
And according to
,
With
, calculate
Coordinate and the interior vertex of a cone that contains circular cone
Coordinate; This moment taperness error
=
Step 3: the quantity of judging low value contact point in the low value contact point set whether less than 2 or high value contact point set in the quantity of high value contact point whether less than 2;
If the quantity of the quantity of low value contact point and high value contact point jumps to step: 6 all greater than 2;
If the quantity of low value contact point less than 2 or the quantity of high value contact point less than 2, carry out coordinate transform, make
With coordinate system
zThe axle forward is in the same way parallel, each measuring point
Become after the change
, jump to next step.
Step 4: respectively with each measuring point be the summit, with
For semi-cone angle, with
Be the axis direction vector, construct circumscribed auxiliary circular cone, do
Auxiliary plane, calculate each circumscribed auxiliary circular cone and plane
Common factor, its common factor is one and cut hands over circle, the cutting of all circumscribed auxiliary circular cone correspondences handed over circle to constitute to cut and handed over the circle set
Respectively with each measuring point be the summit, with
For semi-cone angle, with
Be the axis direction vector, the auxiliary circular cone of structure inscribe; Do
Auxiliary plane, calculate the auxiliary circular cone of each inscribe and plane
Common factor, its common factor is one and cut hands over circle, the cutting of the auxiliary circular cone correspondence of all inscribes handed over circle to constitute to cut and handed over the circle set
Step 5: will gather respectively
,
In the circular projection of cut handing over be parallel to arbitrarily
XoyOn the plane of coordinate plane, obtain cutting and hand over circle to gather
,
On projection plane, calculate 1 donut, satisfy interior circle and the set of donut
In 2 cut to hand over circle circumscribed, the cylindrical of donut and set
In 2 cut to hand over the circle inscribes, the line at two point of contacts that the line at two point of contacts that the interior circle of donut is corresponding is corresponding with the cylindrical of donut has and intersects; According to concentrically ringed central coordinate of circle,
Calculate
,
Jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Direction vector
With
zAfter axle is parallel, high value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
,
zAxial coordinate increases progressively, and makes
,
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Or
The rotation variation of containment region is set
Initial value.
Step 7: calculate
Around
Or
Rotation
Vector after the angle
With
,
Be the vertex of a cone, with
For the axis direction vector, with
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
,
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
,
,
,
Shadow is on any a certain plane perpendicular to axis
On, obtain respectively
,
,
,
, will cut and hand over circular projection on the plane
On; Can set up the binary nonlinear system of equations by following relation,
Wherein
,
Be respectively
,
Corresponding cross section radius of circle,
After change
On the plane
Projection; By finding the solution Nonlinear System of Equations, can calculate
Coordinate; According to
,
,
,
With
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
,
According to the method for step 2, calculate the distance of low value contact point female surface outside containment region
, calculate the high distance that is worth contact point female surface outside containment region
And then according to the method for step 2, calculate the distance of all noncontact measuring points female surface outside containment region successively
If
And
, then represent the variation deficiency, the anglec of rotation
Become
If
Or
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Become
Judge
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
If
The difference of the iterative value that front and back are 2 times is less than the error permissible value
, illustrate and find the 5th contact point, then will
,
,
Assignment is given respectively
,
,
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
,
, then each low value contact point all satisfies following formula,
Each low value contact point all satisfies following formula,
More than in two formulas
,
,
With
,
,
,
,
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge that whether high value contact and low value contact point quantity sum are more than or equal to 6;
If high value contact and low value contact point contact point quantity sum are more than or equal to 6, with in the contact point set 5 be 1 combination, be calculating object with 5 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 8,9 is adjusted
Size; If
Less than the error permissible value of setting
, judge whether to satisfy criterion, jump to step 11 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
, judge that again iteration is gone down successively; If
Greater than the error permissible value of setting
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 6.
Step 11: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Beneficial effect of the present invention is: the contact point relative position that this method inquires satisfies the Minimum Area criterion, and parameter and the taperness error of the actual circular cone corresponding ideal circular cone that calculates are optimal value, and computational stability is good, counting yield is high.
To those skilled in the art, according to use design disclosed by the invention, can easily carry out various distortion and change to the present invention program, should be noted in the discussion above that all these distortion and change all should belong to scope of the present invention.
Embodiment
Embodiment 1:
A kind of computing method of the part conicity based on Minimum Area when cone angle is variable, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
, wherein
=1,2 ...,
n,
nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Form the measuring point collection
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
, the circular cone axis direction vector
And semi-cone angle
Wherein
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Step 2: use following formula, calculate each measuring point successively
Distance to circular conical surface
,
Wherein
, all measuring point correspondences
Form set
Record respectively
,
Corresponding measuring point, institute's record
Corresponding measuring point forms the low value contact point set of containment region
, institute's record
Corresponding measuring point forms the high value contact point set of containment region
And according to
,
With
, calculate
Coordinate and the interior vertex of a cone that contains circular cone
Coordinate; This moment taperness error
=
Step 3: judge that whether the quantity of low value contact point in the set of low value contact point is less than 2;
If the quantity of low value contact point, is pressed the computing method of maximum inscribed circle awl less than 2, inquire about preceding 2 low value contact points, and calculate the parameter of circular cone, jump to step 2;
If the quantity of low value contact point is carried out next step more than or equal to 2.
Step 4: whether the quantity of judging low value contact point in effective low value contact point set equals 2;
If low value contact point quantity equals 2, then 2 low value contact points are effective contact point;
If low value contact point quantity greater than 2, then connects high value contact point and the outer vertex of a cone that contains circular cone respectively
, connect the vertex of a cone of low value contact point and interior containing circular cone respectively
, calculate successively 2 groups of straight lines with arbitrarily perpendicular to
The intersection point on plane, can judgement find 2 low value contact points, the intersection point that connects 2 low value contact point correspondences obtains straight line
l, the intersection point intersection point corresponding with all the other low value contact points that satisfies high value contact point correspondence is distributed in straight line respectively
lBoth sides, if can not find 2 low value contact points that satisfy condition, then jump to step 6; If can find 2 low value contact points that satisfy condition, 2 low value contact points that then satisfy condition are effective contact point, jump to step 5.
Step 5: the intersection point that connects 2 low value contact point correspondences obtains straight line
l 1, and in the corresponding intersection point set of high value contact, inquiry is apart from straight line
l 1Nearest intersection point, then the high value contact point of this intersection point correspondence is effectively high value contact point; 2 effective low value contact points respectively with the vertex of a cone of interior containing circular cone
Link to each other, 2 lines constitute 1 angle, calculate the equidistant point of this angle, and the normal vector of this equidistant point is the direction vector of containment region rotation change
If
Be 1 effective low value contact point wherein,
Be effectively high value contact point;
With 1 noncontact measuring point wherein
Be calculating object, calculate
Equidistant point, and calculate this equidistant point and mistake
And normal vector is
The intersection on plane
, calculate then
Deduct
With
Angle, obtain
Travel through all noncontact measuring points, the calculating correspondence
, all measuring point correspondences
Form set
, in set
Middle element of rejecting less than 0;
Again with a noncontact measuring point
Be calculating object, do
Equidistant point, and calculate this equidistant point and mistake
And normal vector is
The intersection on plane
, calculate then
Deduct
With
Angle, obtain
Travel through all noncontact measuring points, the calculating correspondence
, all measuring point correspondences
Form set
, in set
Middle element of rejecting less than 0;
Query set
,
In minimum value, minimum value is the rotation variation of containment region
On the direction that cone angle reduces, containment region around
Rotation
After, the parameter of calculating containment region
,
,
,
, jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Direction vector
With
zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
,
zAxial coordinate increases progressively, and makes
,
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Or
The rotation variation of containment region is set
Initial value.
Step 7: calculate
Around
Or
Rotation
Vector after the angle
With
,
Be the vertex of a cone, with
For the axis direction vector, with
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
,
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
,
,
,
Shadow is on any a certain plane perpendicular to axis
On, obtain respectively
,
,
,
, will cut and hand over circular projection on the plane
On; Can set up the binary nonlinear system of equations by following relation,
Wherein
,
Be respectively
,
Corresponding cross section radius of circle,
After change
On the plane
Projection; By finding the solution Nonlinear System of Equations, can calculate
Coordinate; According to
,
,
,
With
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
,
According to the method for step 2, calculate the low value contact point contains circular cone outside containment region distance
, calculate high value contact point contains circular cone outside containment region distance
And then according to the method for step 2, calculate all noncontact measuring points contain circular cone outside containment region distance successively
If
And
, then represent the variation deficiency, the anglec of rotation
Become
If
Or
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Become
Judge
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
If
The difference of the iterative value that front and back are 2 times is less than the error permissible value
, illustrate and find the 5th contact point, then will
,
,
Assignment is given respectively
,
,
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
,
, then each low value contact point all satisfies following formula,
Each low value contact point all satisfies following formula,
More than in two formulas
,
,
With
,
,
,
,
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge whether high value contact equals 6 with low value contact point quantity sum;
If high value contact is not equal to 6 with low value contact point quantity sum; Jump to step 12; Otherwise carry out dimensional variations, set the dimensional variations amount
Initial value.
Step 11: the method in the applying step 9, with
,
,
,
,
,
Be unknown quantity, set up Nonlinear System of Equations, error of calculation containment region width is
The time the containment region parameter;
The method of applying step 7 has judged whether that according to change back containment region parameter measuring point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If less than, illustrate and find the 7th contact point, jump to step 12; Otherwise, carry out dimensional variations again, the operation of repeating step 11.
Step 12: judge that whether high value contact and low value contact point quantity sum are more than or equal to 7;
If high value contact and low value contact point contact point quantity sum are more than or equal to 7, with in the contact point set 6 be 1 combination, be calculating object with 6 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 10,11 is adjusted
Size; If
Less than the error permissible value of setting
, judge whether to satisfy criterion, jump to step 13 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
, judge that again iteration is gone down successively; If
Greater than the error permissible value of setting
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 7.
Step 13: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Embodiment 2:
A kind of computing method of the part conicity based on Minimum Area, similar substantially with the calculation process of embodiment 1 when cone angle is constant, difference is to keep cone angle constant in the containment region change, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
, wherein
=1,2 ...,
n,
nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Form the measuring point collection
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
, the circular cone axis direction vector
According to drawing information, obtain semi-cone angle
Wherein
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Step 2: use following formula, calculate each measuring point successively
Distance to circular conical surface
,
Wherein
, all measuring point correspondences
Form set
Record respectively
,
Corresponding measuring point, institute's record
Corresponding measuring point forms the low value contact point set of containment region
, institute's record
Corresponding measuring point forms the high value contact point set of containment region
And according to
,
With
, calculate
Coordinate and the interior vertex of a cone that contains circular cone
Coordinate; This moment taperness error
=
Step 3: the quantity of judging low value contact point in the low value contact point set whether less than 2 or high value contact point set in the quantity of high value contact point whether less than 2;
If the quantity of the quantity of low value contact point and high value contact point jumps to step: 6 all greater than 2;
If the quantity of low value contact point less than 2 or the quantity of high value contact point less than 2, carry out coordinate transform, make
With coordinate system
zThe axle forward is in the same way parallel, each measuring point
Become after the change
, jump to next step.
Step 4: respectively with each measuring point be the summit, with
For semi-cone angle, with
Be the axis direction vector, construct circumscribed auxiliary circular cone, do
Auxiliary plane, calculate each circumscribed auxiliary circular cone and plane
Common factor, its common factor is one and cut hands over circle, the cutting of all circumscribed auxiliary circular cone correspondences handed over circle to constitute to cut and handed over the circle set
Respectively with each measuring point be the summit, with
For semi-cone angle, with
Be the axis direction vector, the auxiliary circular cone of structure inscribe; Do
Auxiliary plane, calculate the auxiliary circular cone of each inscribe and plane
Common factor, its common factor is one and cut hands over circle, the cutting of the auxiliary circular cone correspondence of all inscribes handed over circle to constitute to cut and handed over the circle set
Step 5: will gather respectively
,
In the circular projection of cut handing over be parallel to arbitrarily
XoyOn the plane of coordinate plane, obtain cutting and hand over circle to gather
,
On projection plane, calculate 1 donut, satisfy interior circle and the set of donut
In 2 cut to hand over circle circumscribed, the cylindrical of donut and set
In 2 cut to hand over the circle inscribes, the line at two point of contacts that the line at two point of contacts that the interior circle of donut is corresponding is corresponding with the cylindrical of donut has and intersects; According to concentrically ringed central coordinate of circle,
Calculate
,
Jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Direction vector
With
zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
,
zAxial coordinate increases progressively, and makes
,
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Or
The rotation variation of containment region is set
Initial value.
Step 7: calculate
Around
Or
Rotation
Vector after the angle
With
,
Be the vertex of a cone, with
For the axis direction vector, with
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
,
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
,
,
,
Shadow is on any a certain plane perpendicular to axis
On, obtain respectively
,
,
,
, will cut and hand over circular projection on the plane
On; Can set up the binary nonlinear system of equations by following relation,
Wherein
,
Be respectively
,
Corresponding cross section radius of circle,
After change
On the plane
Projection; By finding the solution Nonlinear System of Equations, can calculate
Coordinate; According to
,
,
,
With
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
,
According to the method for step 2, calculate the distance of low value contact point female surface outside containment region
, calculate the high distance that is worth contact point female surface outside containment region
And then according to the method for step 2, calculate the distance of all noncontact measuring points female surface outside containment region successively
If
And
, then represent the variation deficiency, the anglec of rotation
Become
If
Or
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Become
Judge
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
If
The difference of the iterative value that front and back are 2 times is less than the error permissible value
, illustrate and find the 5th contact point, then will
,
,
Assignment is given respectively
,
,
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
,
, then each low value contact point all satisfies following formula,
Each low value contact point all satisfies following formula,
More than in two formulas
,
,
With
,
,
,
,
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Assignment is given
If there is not measuring point to exceed containment region, then will
Assignment is given
Judge
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
If
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge that whether high value contact and low value contact point quantity sum are more than or equal to 6;
If high value contact and low value contact point contact point quantity sum are more than or equal to 6, with in the contact point set 5 be 1 combination, be calculating object with 5 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 8,9 is adjusted
Size; If
Less than the error permissible value of setting
, judge whether to satisfy criterion, jump to step 11 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
, judge that again iteration is gone down successively; If
Greater than the error permissible value of setting
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 6.
Step 11: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.